“Divide and conquer” semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

Abstract

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

Vibrational investigation of nucleobases by means of divide and conquer semiclassical dynamics

“…For this reason, the initial kinetic energy of the first seven lowest frequency vibrational modes is set to zero, since rotational contributions would jeopardize the numerical convergence of the spectra. This strategy is similar to what has been done in previous semiclassical calculations, 70,71 and it does not represent a bias since the initial kinetic energy of the trajectory is reduced by only 5% below the harmonic ZPE value, which is obviously in excess with respect to the actual ZPE. The columns of Tables II and III, labeled "Harmonic", report the harmonic frequencies of both isomers.…”

Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation

“…110 According to Ref. 41, sampling subspaces are chosen to be the O-H stretching sector, the bending sector, the proton transfer mode, the proton perpendicular sector, the O-O stretching mode. Variants of these choices are indicated when discussing the results.…”

Protonated glycine supramolecular systems: the need for quantum dynamics

“… 48 The method can deal with very high dimensional molecular and supra-molecular systems, and it is very accurate when compared to available exact vibrational quantum mechanical calculations. 49 , 50 Specifically, our DC-SCIVR method has been tested successfully against systems with up to hundreds of degrees of freedom, 48 and in particular it has been employed to study the vibrational features of the protonated water dimer, the Zundel cation. The results are very accurate (within a few wavenumbers) even for the vibrational bands of the proton doublet in the region of the O–H–O stretching frequency and associated with the proton transfer (∼1000 cm –1 ), when compared to exact grid-based quantum dynamics results on the same PES.…”

“…First, full dimensional ab initio on-the-fly classical trajectories are calculated. Then, the normal modes are divided into vibrational subspaces according to their mutual coupling, 48 , 49 , 51 and the partial spectra are calculated by projecting the classical trajectory information according to the following formula 48 where F is the dimensionality of the vibrational subspace, and the multi-dimensional phase-space integration is characterized by a positive-definite time-dependent integrand made of the classical action ( S[combining tilde] t ( p[combining tilde] (0), q[combining tilde] (0))), the phase of the semiclassical prefactor ( ϕ̃ t ), 46 and the overlap between the reference state | Ψ̃ 〉 and the coherent state | and the coherent state | p[combining tilde] ( t ), q[combining tilde] ( t ))〉. More details can be found in the ESI.. More details can be found in the ESI.…”